Applications
in Multivariate Time Series Analysis and Forecasting: SSA

Singular Spectrum Analysis (SSA) is a powerful method of time
series analysis and forecasting. It combines advantages of many other
methods, such as Fourier and regression analyses, with simplicity of
visual control aids. The basic SSA algorithm for analyzing time series
consists of:

Transformation of the time series into a matrix using the
moving window;

Singular Value Decomposition (SVD) of this matrix;

Reconstruction of the original time series based on
selected eigentriples.

The two
techniques used in SSA (SVD and the reconstruction procedure) are
optimal in a natural class of techniques of multivariate analysis. The
result of the SSA processing is a decomposition of the time series into
several components, which can often be identified as trends,
seasonalities and other oscillatory series, or noise components. This
decomposition initializes forecasting procedures for both the original
time series and its components. The method can be naturally extended to
multidimensional time series and to image processing.

The method is a powerful and useful tool of time series
analysis in meteorology, hydrology, geophysics, climatology, economics,
biology, physics, medicine and other sciences. It can be used for the
series that are short and long, one-dimensional and multidimensional,
stationary and nonstationary, almost deterministic and noisy.

Current interests in the cluster concentrate around the
following topics:

Perturbation analysis in SSA and related techniques

Multivariate SSA and its applications to econometrics

Application of SSA to the analysis of images

SSA as a change-point detection technique

Sensitivity of SSA forecasting formulas to the noise level

Application of SSA for finding structure in human genome studies

Comparison of SSA with ARIMA and other standard techniques
of time series analysis and forecasting